Roll the chicken livers on the flour. They should be coated well with flour.

Meanwhile, heat the olive oil and butter in a medium sized pan. Saute the livers, turn them occasionally. While you're frying the livers, cover it with a paper towel since the oil will spit. Add the walnuts into the pan, stir. Then pour the vinegar and garlic mixture, stir. When the smell of garlic comes out, turn the heat off. Take them out with a perforated spoon and place on a paper towel to soak up extra oil. Season them with cayenne pepper and salt. Serve the Fried Chicken Livers with Walnuts with the Onion Salad by the side.